Question:
If a metal crystallises in bcc structure with edge length of unit cell $4.29 \times 10^{-8}\, cm$ the radius of metal atom is
If a metal crystallises in bcc structure with edge length of unit cell $4.29 \times 10^{-8}\, cm$ the radius of metal atom is
Updated On: May 13, 2024
- $3.2 \times 10^{-7}\,cm$
- $1.86 \times 10^{-8}\,cm$
- $1.07 \times 10^{-7}\,cm$
- $1.07 \times 10^{-8}\,cm$
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The Correct Option is B
Solution and Explanation
Key Idea The relation between edge length and radius of an atom in a $bcc$ structure is related as:
$r=\sqrt{3} / 4 a $
Given, $a=4.29 \times 10^{-8} cm$
For bcc structure,
$r =\frac{\sqrt{3}}{4} a=\frac{\sqrt{3}}{4} \times 4.29 \times 10^{-8} cm$
$=1.857 \times 10^{-8} cm \simeq 186 \times 10^{-8} cm$
$r=\sqrt{3} / 4 a $
Given, $a=4.29 \times 10^{-8} cm$
For bcc structure,
$r =\frac{\sqrt{3}}{4} a=\frac{\sqrt{3}}{4} \times 4.29 \times 10^{-8} cm$
$=1.857 \times 10^{-8} cm \simeq 186 \times 10^{-8} cm$
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Concepts Used:
Unit Cells
The smallest portion of a crystal lattice which repeats in different directions to form the entire lattice is known as Unit cell.
The characteristics of a unit cell are:
- The dimensions are measured along the three edges, a, b and c. These edges can form different angles, they may be mutually perpendicular or may not.
- The angles held by the edges are α (between b and c) β (between a and c) and γ (between a and b).
Therefore, a unit cell is characterised by six parameters such as a, b, c and α, β, γ.
Types of Unit Cell:
Numerous unit cells together make a crystal lattice. Constituent particles like atoms, molecules are also present. Each lattice point is occupied by one such particle.
- Primitive Unit Cells: In a primitive unit cell constituent particles are present only on the corner positions of a unit cell.
- Centred Unit Cells: A centred unit cell contains one or more constituent particles which are present at positions besides the corners.
- Body-Centered Unit Cell: Such a unit cell contains one constituent particle (atom, molecule or ion) at its body-centre as well as its every corners.
- Face Centered Unit Cell: Such a unit cell contains one constituent particle present at the centre of each face, as well as its corners.
- End-Centred Unit Cells: In such a unit cell, one constituent particle is present at the centre of any two opposite faces, as well as its corners.